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Abstract

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Let P(D) be a partial differential operator with constant coefficients which is surjective on the space A(Ω) of real analytic functions on an open set Ω⊂ℝn. Then P(D) admits shifted (generalized) elementary solutions which are real analytic on an arbitrary relatively compact open set ω ⊂ ⊂ Ω. This implies that any localization Pm,Θ of the principal part Pm is hyperbolic w.r.t. any normal vector N of ∂Ω which is noncharacteristic for Pm,Θ. Under additional assumptions Pm must be locally hyperbolic.